In conventional X-ray tomography the apparatus produces images of a single slice of an object by moving an X-ray camera and the image plate in a complementary manner so that everything is blurred except for a predetermined plane. Commercial machines produce images of a number of separate slices, moving the X-ray machine to produce a planar picture and then moving the object under test in the Z direction to produce a planar picture at different slices. That needs more total pictures than the views spread over a solid angle and it produces a cruder representation of a three-dimensional image because volume cells intermediate between slices have to be derived by interpolation.
Conventional tomography thus produces images of discrete slices normal to the axis of objects of short axial length. It is more common, however, to require images to discrete slices normal to the axis of a long object. The established form of computer tomography (CT) is designed to do this. It does it by taking a number line images, at different viewing angles in the plane of each such slice (typically 360-1440 views, taken at 1.degree. to 1/4.degree. intervals). These are then used to compute the corresponding slice image. However, the invention--and even the established form of computer tomography--is better understood by first postulating an extension of computer tomography which, unlike existing systems, would produce a true three-dimensional mapping of the X-ray densities (i.e. opacities) of a complete set of symmetrical, equally-spaced volume cells (voxels), in place of merely producing such information for each of a limited number of parallel slices through the relevant object. This hypothetical version of computer tomography might map a cubical volume L.sup.3 into (L/c).sup.3 voxels of size c.sup.3. In its simplest form, this postulated ideal form of computer tomography would involve L/c distinct X-ray projections, of (L/c).sup.2 pixels. Each pixel represents the aggregate density of a column of L/c voxels. The individual densities of all voxels are then computed by (L/c).sup.3 simultaneous equations. No assumptions about the features of the specimen are involved. The resulting picture is fully three-dimensional, amenable to three-axis rotation, slicing etc.
In practice, the voxels are not independent: signal/noise considerations require a significant degree of smoothing and integration (by the human eye or brain and/or by a computer algorithm), which causes the effective image to be composed of reasonably smooth multi-voxel elements.
We have found that it is possible to make use of this assumption to simplify data extraction, storage and processing.
The processing may be simplified by treating an object under test as a set of component objects, each defined by one or more closed surfaces, where the precision of the surface shape of these component objects should ideally match the resolution of the sensor system. Indeed, for smoothly-varying surfaces, a least mean-squares or similar fit can produce a precision superior to that of the individual constituent measurements. Furthermore these component objects are generally of individually uniform specific density, and of reasonably "well-behaved" shape. (Complex shapes may be broken down into multiple constituent objects of simpler shape.)
These component objects can be cross-identified, between different views, by projection on to the axis common to each pair of such views. Each such projection also defines the three-dimensional position of two outermost surface points of the object (as projected on to this common axis), with a precision matching that of the source pictures. Thus n views generate n(n-1) such points on each object surface, and these points cluster most closely in the areas of greatest curvature on these surfaces. The line contour segments between the points can also be derived with considerable precision. This generates a network of n(n-1)+2 surface cells, The three-dimensional shape of these cell surfaces can also be derived with good precision. (If there are any inflexions or sharp corners or other point singularities, their position in three dimensions can similarly be identified from any two suitable projections, thus producing some additional nodes and meshes in this network.)
On this basis, about ten views, yielding 92 cells per surface, are likely to be to be sufficient for most applications. At the other extreme, 32 views (still a minute number compared with conventional computer tomography) would generate 994 cells. This permits the use of much simpler algorithms to generate the network of line-segments linking the points and to derive the surface of the resulting mesh cells. We have found, in practice, tolerable reconstructions can be obtained with as few as five source images, whilst anyone wishing to ignore the curvature of line segments might wish to use up to 100 source views.
The representation of the observation volume as a set of three-dimensional objects matches the physical reality. This enables the technique to cope with higher noise levels than equivalent conventional systems. It also provides a convenient basis for determining specific densities and for providing user-friendly facilities of object selection, enhancement, rotation, slicing, and general manipulation.
It is possible to regard a specimen as composed of a limited number of solid "objects", which each:
1. Comprise a substantial number of voxels; PA1 2. Have a reasonably "well-behaved" geometric shape; PA1 3. Have a reasonably smoothly-varying projected density.
When applying the invention to X-rays, used for medical applications, a significant proportion of clinical situations match this scenario. A single functional physiological entity of more complex shape will then normally comprise two or more "objects" of this type. Diagnosable anomalies are departures from the expected size, shape and density of these objects or the presence of "unscheduled" extra objects. The requisite three-dimensional information can be extracted from, say, about ten X-ray projections from different directions.
The resultant picture is amenable to three-axis rotation and to slicing, just as with three dimensional pictures extrapolated from conventional forms of tomography. In addition, however, any desired subset of objects can be readily selected or deleted (or enhanced, attenuated or colored) at the user's discretion. Thus this approach gives the benefits of conventional forms of tomography--and some further user-friendly features--with dramatically fewer X-ray exposures and reduced computation.